Capital One·Machine Learning Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Capital One ML Engineer interview that came down to a tree traversal problem. Nothing groundbreaking but they wanted you to actually talk through both approaches and the tradeoffs, not just code one and call it done.

Questions Asked (1)

Given the root of a binary tree, return all root-to-leaf paths. Each path should be represented as a string with node values joined by '->'. Walk through both a DFS backtracking approach and a BFS path-tracking approach, and compare their time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The coding part was fine but they pushed hard on the complexity analysis for both approaches.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem and edge cases, then explain the DFS backtracking approach with a recursive helper that builds paths and backtracks, followed by the BFS approach using a queue of (node, path) pairs. Compare their time and space complexities, noting that both are O(N) time and O(N) space in the worst case, but with different constant factors and memory profiles.

Pro tip: Mention that DFS backtracking is more memory-efficient for deep, narrow trees, while BFS can use more memory for wide trees due to storing many partial paths; also note that string concatenation in BFS can be costly, so using a list of values and joining at the end is better.

1. Clarify and Define

Confirm the definition of a root-to-leaf path (starts at root, ends at a leaf node) and discuss edge cases like an empty tree or a single-node tree. Ask if the output should be a list of strings.

2. DFS Backtracking Approach

Explain a recursive DFS that maintains a current path list. At each node, append its value; if it's a leaf, convert the path to a string and add to results; otherwise, recurse on children; then backtrack by popping the value.

3. BFS Path-Tracking Approach

Describe using a queue that stores pairs of (node, current_path_string or list). Start with the root and its value. While the queue is not empty, dequeue, and if it's a leaf, add the path to results; otherwise, enqueue children with updated paths.

4. Complexity Analysis

Analyze both approaches: Time O(N) where N is number of nodes, as each node is visited once. Space O(N) for the output in the worst case (e.g., a complete binary tree has O(N) leaves), plus recursion stack O(H) for DFS and queue size O(N) for BFS. Discuss how string concatenation affects time in BFS if done naively.

5. Compare and Conclude

Summarize trade-offs: DFS uses less memory for deep trees and is simpler to implement recursively; BFS may be more intuitive for level-order thinking but can use more memory for wide trees. Mention that both are acceptable, but DFS is often preferred for this problem.

Key Points to Mention

Time complexity is O(N) for both approaches because each node is visited exactly once.
Space complexity includes the output size, which can be O(N) in the worst case (e.g., a full binary tree with N/2 leaves).
DFS backtracking uses O(H) extra space for the recursion stack, where H is tree height, which is O(log N) for balanced trees and O(N) for skewed trees.
BFS queue can hold up to O(N) nodes in the worst case (e.g., a complete binary tree's last level), and each stored path can be O(H) long, leading to O(N*H) space in naive implementations.
String concatenation in BFS can lead to O(N^2) time if not careful; using a list of values and joining at the end is more efficient.
Edge cases: empty tree returns empty list; single node returns ["value"]; paths should not include '->' at the end.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.